Modeling with variation: write an equation describing a direct relationship where $y$ varies directly as the cube of $x$ and when $x=36$, $y=24$

Question

I am to write an equation describing a direct relationship where $y$ varies directly as the cube of $x$ and when $x=36$, $y=24$

The solution provided at the back of my book says $y=10x^3$, I am unable to arrive at this. My working…

General formula (find $k$):
$$y=kx^n$$
Plugging in:
$$y=kx^3$$
$$24=k36^3$$
$$24=46656K$$
$$k=\frac{24}{46656}$$

I arrive at a very different value of $k$. How can I arrive at $k=10$ per my textbooks solution?
$$$$

Answer 1

If $y=kx^3$, then $$ k=\frac{y}{x^3}=\frac{24}{36^3}=\frac{24}{46656}=\frac{1}{1944}. $$ So definitely not $10x^3$.